The woman had hired the car on Thursday to return home after visiting her husband who was in hospital.
Deputy Commissioner of Police (eastern suburban division) S Bandopadhyay said the driver, instead of taking her home to Entally, drove to Rajarhat and allegedly raped her.
The driver dropped the woman at Entally on Friday morning and sped away.
Bandopadhyay said the woman then approached a traffic constable who took her to the Entally police station where she filed a complaint of rape.
Joint Commissioner of Police (crime) Pallab Kanti Ghosh told PTI that the driver was traced and arrested on the basis of the complaint.
The police said the woman would be medically examined and the driver will be produced in the court on Saturday.
In February, an Anglo-Indian woman was allegedly raped in a car while returning home from a night club in Park street, which led to tremendous public outcry.